I do not understand what this regular language is asking for? Find a grammar for L (G) = {w || w | is odd, Σ = (0, 1)}

Yes, I can see why that would be confusing. Typographic composition is probably making this more difficult to follow. I guess what is written is $ {w mid | w | text {is odd}, ldots } $. This is the set of all $ w $ such that $ | w | $ It is strange, etc. Here $ | w | $ usually represents the length of the word $ w $.

It could have been clearer if the author had used two points instead of a vertical line in our set creator notation: then it would have been written $ {w: | w | text {is odd}, ldots } $, and maybe it would be easier to see what is happening …